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Volumn 83, Issue 7, 2011, Pages

Topological phases of fermions in one dimension

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EID: 79961067002     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.075103     Document Type: Article
Times cited : (1034)

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    • Here we follow Dyson's philosophy (Ref. 30). In fact, he also found ten symmetry classes, though a coarser division into only three classes appears in the final answer. This is because Dyson considers the action of symmetries on the Hilbert space of a many-body system. Unlike the Nambu space, the Hilbert space of quantum states has no canonical conjugation, since the multiplication by a phase is an intrinsic symmetry.
    • Here we follow Dyson's philosophy (Ref. 30). In fact, he also found ten symmetry classes, though a coarser division into only three classes appears in the final answer. This is because Dyson considers the action of symmetries on the Hilbert space of a many-body system. Unlike the Nambu space, the Hilbert space of quantum states has no canonical conjugation, since the multiplication by a phase is an intrinsic symmetry.
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    • -, or by changing k to 2-k. We have chosen not to do that because the variable change k2-k is convenient in the free-fermion context; see Ref. 2.
    • -, or by changing k to 2 - k. We have chosen not to do that because the variable change k 2 - k is convenient in the free-fermion context; see Ref. 2. © 2011 American Physical Society.


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